The present invention relates to an interferometric determination of a transfer function of a device under test (DUT), in particular to an interferometric determination of a transfer function of a DUT to evaluate an impulse response of the DUT.
A standard routine of the prior art when determining a transfer function of a DUT was published by Heffner, B. L. in “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis”, IEEE Photonics Technology Letters, 1992, 4, p. 1066-1069, and in “Deterministic, analytically complete measurement of polarization dependent transmission through optical devices”, IEEE Photonics Technology Letters, 1992, 4, p. 451-454. The routine applies the so called “Jones algorithm” published by Jones, R. C. in “A new calculus for the treatment of optical systems, VI: Experimental determination of the matrix”, Journal of Optical Society of America, 1947, 37, p. 110-112, to calculate amplitude and group delay eigenvalues of the DUT and from these determines the two eigenvalue transfer functions h1(ω) and h2(ω) of the DUT according to the equations of FIG. 8, with amp1 and amp2 being the amplitude eigenvalues, ω being the optical frequency and φ1 and φ2 being the phase eigenvalues. Knowledge of the two eigenvalue transfer functions h1 and h2 allows the calculation of the impulse response eigenvalues for the two eigenstates. This procedure works well for a DUT consisting of a single response.
However, the interferometric determination of a transfer function for calculation of an impulse response of a DUT is complicated, if the DUT consists of multiple transfer function elements, either due to reflective parts at different locations when performing reflectometry or due to a propagation splitting with different path lengths when performing transmission. In case of multiple transfer function elements one gets multiple responses. For these multiple responses the above algorithm falls, because in the optical frequency domain these responses are not separable any more and the computation of a single eigenvalue pair as a function of λ (or ω) makes no sense and the output becomes chaotic (see e.g. FIGS. 2 and 3). Multiple responses overlapping in the optical frequency domain can not be represented by a single eigenvalue pair in the optical frequency domain.
For a better understanding this drawback of the prior art is demonstrated with a measurement setup shown in FIG. 1. An optical signal 2 generated by a tunable laser (TLS) 1 and transmitted through a polarization controller 3 and a fiber 4 is split by a first beam splitter 6 into a measurement signal 7 propagating in an upper DUT-arm 8 and into a reference signal propagating in a reference arm 10. An exemplary DUT, symbolized by a box of dashed lines, consisting of a polarization maintaining (PM) fiber 8 transports the optical signal 2 and generates two signal peaks A and B delayed to each other in time domain by 2 ps which is symbolized by two curves A and B in FIG. 1.
This simplified DUT inhibits the properties birefringence and multipath transmission occurring in passive optical components for fiber telecommunication (interleaver, multiplexer). The measurement signal 7 is split by a second beam splitter 12 positioned in arm 8 into sub-signals 14 and 16 propagating in an upper sub-arm 18 and a lower sub-arm 20 of upper measurement arm 8. Sub-arm 18 and sub-arm 20 are each made of single mode fiber (SMF). In FIG. 1 small arrows at the curves 14 and 16 indicate the orientation of principal states of polarization (PSPs) of the sub-signals 14 and 16.
With a third beam splitter 22 sub-signals 14 and 16 are recombined to a resulting signal 24 with a substantial delay of about 30 ps between the two sub-signals 14 and 16 since lower sub-arm 20 is 6 mm shorter than upper sub-arm 18. Signal 24, i.e., sub-signals 14 and 16, and the reference signal of reference arm 10 are recombined by a fourth beam splitter 26 to an interferogram or interference signal 28. The interference signal 28 is split by a polarization beam splitter (PBS) 30 into two signals 32 and 34. Signal 32 is detected by a detector 36 and signal 34 is detected by detector 38. The PBS 30 together with the two detectors 36 and 38 represents a polarization diversity receiver (PDR). Both PDR arms 36 and 38 are connected to an evaluation unit (not shown) to analyze the interferogram and generate a Fourier spectrum of the interferogram.
In the Fourier spectrum two peak objects of comparable height will be observed. Additional interferences between these two peak objects will appear at lower frequencies and are here neglected (e.g. high pass filtered). Because the orthogonal PDRs 36 and 38 are not aligned with the individual PSPs of the two peak objects each PDR will see a rotated mixture. Therefore, the computation of group delay (GD), differential group delay (DGD) and amplitude eigenvalues by the evaluation unit yields artifacts that do not allow to extract correct impulse responses from the transfer functions. These artifacts are shown in FIGS. 2-4. FIG. 2 shows the GD, FIG. 3 shows the DGD and FIG. 4 shows the amplitudes of the impulse response calculation based on the GD of FIG. 2. In FIG. 4 instead of two main peaks separated due to the path difference between fiber 18 and 20 with a 2 ps split fine structure an artificial peak comb structure is generated. The structure shown in FIG. 4 is accidentally and may vary by slightly changing the positions and therefore the polarization states of the fibers used for the interferometric setup.